I have a 2D line, which is determined by the following set of points.

x y z
0 0 0
1 1 0
2 4 0
3 9 0
4 16 0

and would like to extrude it in the z direction. Ie so that I get a surface that if you look at it from the z direction you see the above profile but has depth in the z direction.

I’m new to blender so this may seem basic to some…

Depends if your line is a mesh or a curve object. If its a mesh, in edit mode select all the vertices, press E to extrude, Z to constrain along the z axis and either type a number or move your mouse to control the amount of extrusion.
If you have a curve, first convert to a mesh with Alt+C